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# Pressure and Force

## Pressure is a force spread out over an area. A small force applied over a very small area can exert a large force.

Estimated7 minsto complete
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Progress
Practice Pressure and Force
Progress
Estimated7 minsto complete
%
Pressure and Force

Students will learn the difference between pressure and force and how to calculate the pressure in a variety of problems

### Key Equations

\begin{align*}P = \frac{F}{A}\end{align*} ; Pressure is a force exerted over some area

Guidance
Pressure is often confused with force. Pressure is force spread out over an area; a small force exerted on a very small area can create a very large pressure; i.e., poke a pin into your arm!

#### Example 1

How much pressure does a 340-g Coke can exert on a table if the diameter of the can is 8.0 cm?

Question: \begin{align*}P = ? [Pa]\end{align*}

Given: \begin{align*}m = 340\ grams = 0.340\ kg\end{align*}

\begin{align*}{\;}\qquad \quad \text{diameter} = 8.0\ cm = 0.08\ m\end{align*}

\begin{align*}{\;}\qquad \quad g = 10\ m/s^2\end{align*}

Equations: \begin{align*}P = \frac{F}{A}\end{align*} Area of a circle: \begin{align*}A = \pi \cdot r^2\end{align*}

Plug n’ Chug: \begin{align*}P = \frac{F}{A} = \frac{mg}{ \pi \cdot r^2} = \frac{(0.340 \ kg)\left (10 \frac{m}{s^2} \right )}{\pi \left (\frac{0.08 \ m}{2} \right )^2}= \left (\frac{3.4 \frac{kg \cdot m}{s^2}}{5.0 \times 10^{-3} m^2} \right ) = 680 \frac{N}{m^2} = 680 \ Pa\end{align*}

Answer: \begin{align*}\boxed{\mathbf{680 \ Pa}}\end{align*}

### Time for Practice

1. Why does a sharp knife cut so much better than a dull one?
2. Every day Fakir likes to spend about an hour meditating on his bed of nails. Fakir’s mass is 60 kg, his bed contains 2000 nails, and each nail point has a surface area of \begin{align*}4 \ mm^2\end{align*}.
1. Calculate the total surface area of all the nail points, then convert that area into square meters.
2. Calculate the pressure exerted on Fakir by the nails. Compare this to your answer from the previous question.
3. Estimate the pressure in Pascals that you exert on the ground when you stand in your bare feet flat compared to 'tippy toes'. Clearly state your assumptions.

2. a. \begin{align*}0.008 \ m^2\end{align*} b. 75 kPa